BIonic membranes and AdS instabilities

TL;DR

This paper investigates the stability of certain AdS$_4$ flux compactifications in type IIA string theory, analyzing membrane interactions and decay processes to understand non-perturbative stability of these vacua.

Contribution

It extends explicit 10d solutions to a family of perturbatively stable non-supersymmetric vacua and analyzes their non-perturbative stability via membrane dynamics.

Findings

D4-branes and anti-D4-branes feel no force in both $ abla=1$ and $ abla=0$ vacua.

D8-branes with D6-branes ending on them can be superextremal and attracted to the boundary.

Simple $ abla=0$ vacua with space-time filling D6-branes are unstable against bubble nucleation.

Abstract

We study 4d membranes in type IIA flux compactifications of the form AdS$_4 \times X_6$, where $X_6$ admits a Calabi--Yau metric. These models feature scale separation and D6-branes/O6-planes on three-cycles of $X_6$. When the latter are treated as localised sources, explicit solutions to the 10d equations of motion and Bianchi identities are known in 4d $\mathcal{N}=1$ settings, valid at first order in an expansion parameter related to the AdS$_4$ cosmological constant. We extend such solutions to a family of perturbatively stable $\mathcal{N}=0$ vacua, and analyse their non-perturbative stability by looking at 4d membranes. Up to the accuracy of the solution, we find that either D4-branes or anti-D4-branes on holomorphic curves feel no force in both $\mathcal{N} =1$ and $\mathcal{N}=0$ AdS$_4$. Differently, D8-branes wrapping $X_6$ and with D6-branes ending on them can be superextremal 4d membranes attracted towards the $\mathcal{N}=0$ AdS$_4$ boundary. The sources of imbalance are the curvature of $X_6$ and the D8/D6 BIon profile, with both comparable terms as can be checked for $X_6$ a (blown-up) toroidal orbifold. We then show that simple $\mathcal{N}=0$ vacua with space-time filling D6-branes are unstable against bubble nucleation, decaying to $\mathcal{N}=0$ vacua with less D6-branes and larger Romans mass.